Frequency synthesizers provide a way to adjust and control a frequency of a periodic signal, such as a clock. Synthesizers with wide tuning ranges often employ inductor-capacitor (LC) circuits having adjustable parameters, such as an adjustable capacitance. The capacitance may be generated by a capacitor array that exhibits a desired capacitance in response to an N-bit codeword. Typically, each possible codeword is associated with a range of oscillator frequencies. Thus, a 3-bit codeword may have 8 possible sequences, with each possible sequence corresponding to a sub-range of desired frequencies. Selection of a desired frequency is thus dependent on selection of a proper codeword.
To estimate the appropriate capacitor codeword corresponding to a desired frequency setting, conventional methods of frequency synthesis often employ binary search techniques. One conventional binary search algorithm begins by activating the Nth bit of a given capacitor array, often referred to as the most-significant-bit (MSB). The value of the resulting capacitance is used in an LC circuit for the synthesizer, and the frequency determined via an edge counter. The state of the bit is then determined based on the value of the count, with the frequency generally varying in an inversely proportional manner to the capacitance.
In some situations, especially for voltage-controlled-oscillator (VCO) applications, it may be desirable to reduce a gain associated with the VCO. This often increases the resolution and number of bits of the capacitor array. For applications where the number of bits increases, problems relating to errors in frequency estimations may arise. Generally, allowable error in the VCO frequency estimation is inversely proportional to 2N. By increasing the number of bits in the capacitor array, such as by 1, the frequency estimation time doubles. So when the number of bits is increased from N to N+1, the total capacitor search time increases by:(N+1)2N+1/N2N=2(N+1)/N 
Therefore, the capacitor search time increases exponentially with the number of bits in the VCO capacitor codeword. For fast channel switching and stringent locking time requirements, faster methods for estimating a more accurate capacitor codeword are desirable.